Finite Group Databasebeta

← Group #13172048

Character table — Group #13172048

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666668888888888888888121212121212121212121212121212121212121818181818181818242424242424242424242424242424243636363636363636363654547272108
order12223336666666662333666666666662244443666666666666666444666612121212121212121212121244441212121266121212121212121212121212121222446612121212446124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1111111111111111111-111111111-1-111-1-11111111111111-11-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1
χ3111111111111111111111111111111111-1-1111111111111111111-111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-111-111111-1-1-1-111111-11-1-1-111-1-1-1-11-1-1
χ4111111111111111111111111111111111-1-1-1-11111111111111111-11-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-111-1-1-1-1-1-1-1-1-11-1111-1-1-1-111-111
χ51111111111111111111111111111111-1-1111111111111111111111-11-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-11-1-111111111-11-1111-1-1-1-1-1-1-11-1
χ61111111111111111111111111111111-1-111-1-111111111111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-11111-1-1-1-11-11-1-1-111-1-1111-11
χ71111111111111111111111111111111-1-1-1-1111111111111111111-1-11-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-11-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11
χ81111111111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1
χ91111111111111111-1111-1-11111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-11111-1-111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-1-111-1111111-1-1-1-11
χ101111111111111111-1111-1-11111111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1-111111-1-111-1-111-1-1-1-111-1-1-1-1-1-111-11-11-1-111-1-1-1-1111-1-11-1-1-1-1111111-1
χ111111111111111111-1111-1-111111111111-1-1111-1-1-1-1-1-1-1-1111-1-1-1-11-1-11111-1-1-1-111-1-11111-1-1111111111-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-11-1
χ121111111111111111-1111-1-111111111111-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-11-111111-1-1-1-1-1-1-1-1-1-111-1-11111111111-11-1-1-1-111-1-11111-1-111-1-1-1-1-1-11-11
χ131111111111111111-1111-1-1111111111-1-111111-1-1-1-1-1-1-1-1111-1-1-1-1-11-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-11-11111-1-111-1-111-1-111-1-1-1-1111-1-1
χ141111111111111111-1111-1-1111111111-1-111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-11111111-1-1-1-111-1-111-1-111-1-1-1-1-111
χ151111111111111111-1111-1-1111111111-1-1-1-1111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-11-11-111-1-11111-1-11-1-11-1-1-1-111-1-1111
χ161111111111111111-1111-1-1111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-111-111-111111111-1-1-1
χ17222222-1-12222-1-12222-1-1222-1-1-122-1-1-1220022-12-122-1-1-1-1-1-1-1-1-1-1-102222-1-12200-1-100220000000000-1-102-1-1-1-10000-1-1-1-1202000-1-10000-100
χ18222222-1-12222-1-12222-1-1222-1-1-122-1-1-12200-2-2-12-122-1-1-1-1-1-1-1-1-1-1-102-222-1-122001100-2-20000000000-1-10-2-11-1-100001111-20-2000110000100
χ19222222-1-12222-1-12222-1-1222-1-1-122-1-1-1-2-20022-12-122-1-1-1-1-1-1-1-1-1-1-10-22-2-211-2-200-1-10022000000000011021-1110000-1-1-1-1-20-2000110000100
χ20222222-1-12222-1-12222-1-1222-1-1-122-1-1-1-2-200-2-2-12-122-1-1-1-1-1-1-1-1-1-1-10-2-2-2-211-2-2001100-2-20000000000110-2111100001111202000-1-10000-100
χ21222222-1-12222-1-122-22-1-1-2-22-1-1-122-1-1-1220022-1-21-2-21111-1-1-111110-2-222-1-1-2-200-1-100220000000000-1-10-211110000-1-111-202000-1-10000100
χ22222222-1-12222-1-122-22-1-1-2-22-1-1-122-1-1-12200-2-2-1-21-2-21111-1-1-111110-2222-1-1-2-2001100-2-20000000000-1-1021-111000011-1-120-2000110000-100
χ23222222-1-12222-1-122-22-1-1-2-22-1-1-122-1-1-1-2-20022-1-21-2-21111-1-1-1111102-2-2-2112200-1-100220000000000110-2-11-1-10000-1-11120-2000110000-100
χ24222222-1-12222-1-122-22-1-1-2-22-1-1-122-1-1-1-2-200-2-2-1-21-2-21111-1-1-11111022-2-21122001100-2-200000000001102-1-1-1-1000011-1-1-202000-1-10000100
χ2522222-12222-1-122-122-1-1222-1-122-1-1-1-12002222-1-12-1-1-1-122-1-1-1-1-1-1-12020000002222-1-1-1-1220000000000-1-10200-1-1-1-1-1-1-1-10202-1-10000000-10
χ2622222-12222-1-122-122-1-1222-1-122-1-1-1-120022-2-2-1-12-1-1-1-122-1-1-1-1-1-1-120-200000022-2-2-1-111220000000000-110-200-1-1-1-111110-20-211000000010
χ2722222-12222-1-122-122-1-1222-1-122-1-1-1-1200-2-222-1-12-1-1-1-122-1-1-1-1-1-1-1-202000000-2-22211-1-1-2-200000000001-102001111-1-1-1-10-20-211000000010
χ2822222-12222-1-122-122-1-1222-1-122-1-1-1-1200-2-2-2-2-1-12-1-1-1-122-1-1-1-1-1-1-1-20-2000000-2-2-2-21111-2-20000000000110-200111111110202-1-10000000-10
χ2922222-12222-1-122-12-2-1-12-2-2-1-122-1-1-1-12002222-11-21111-2-2-1-1-11111-20-20000002222-1-1-1-1-2-20000000000110-200-1-111-1-111020-2-1-1000000010
χ3022222-12222-1-122-12-2-1-12-2-2-1-122-1-1-1-120022-2-2-11-21111-2-2-1-1-11111-20200000022-2-2-1-111-2-200000000001-10200-1-11111-1-10-202110000000-10
χ3122222-12222-1-122-12-2-1-12-2-2-1-122-1-1-1-1200-2-222-11-21111-2-2-1-1-1111120-2000000-2-22211-1-1220000000000-110-20011-1-1-1-1110-202110000000-10
χ3222222-12222-1-122-12-2-1-12-2-2-1-122-1-1-1-1200-2-2-2-2-11-21111-2-2-1-1-11111202000000-2-2-2-21111220000000000-1-1020011-1-111-1-1020-2-1-1000000010
χ332222-1222-1-122222-12-12-1-1-1-12-1-1-1-122-1222200-122-1-122-1-1-1-1-1-1-1-1-1220-1-122-1-1-1-1002200-1-12222-1-1-1-1-1-12020-1-1-1-1-1-1000000000000-1-100000
χ342222-1222-1-122222-12-12-1-1-1-12-1-1-1-122-122-2-200-122-1-122-1-1-1-1-1-1-1-1-1-220-1-122-1-11100-2-20011-2-2-2-21111-1-1-2020-1-111110000000000001100000
χ352222-1222-1-122222-12-12-1-1-1-12-1-1-1-122-1-2-22200-122-1-122-1-1-1-1-1-1-1-1-12-2011-2-211-1-1002200-1-1-2-2-2-211111120-2011-1-1-1-10000000000001100000
χ362222-1222-1-122222-12-12-1-1-1-12-1-1-1-122-1-2-2-2-200-122-1-122-1-1-1-1-1-1-1-1-1-2-2011-2-2111100-2-200112222-1-1-1-111-20-20111111000000000000-1-100000
χ372222-1222-1-122222-1-2-12-111-12-1-1-1-122-1222200-1-2-211-2-211-1-1-11111-2-20-1-12211-1-10022001122-2-21111-1-1-20-2011-1-111000000000000-1-100000
χ382222-1222-1-122222-1-2-12-111-12-1-1-1-122-122-2-200-1-2-211-2-211-1-1-111112-20-1-122111100-2-200-1-1-2-222-1-1-1-1-1-120-201111-1-10000000000001100000
χ392222-1222-1-122222-1-2-12-111-12-1-1-1-122-1-2-22200-1-2-211-2-211-1-1-11111-22011-2-2-1-1-1-100220011-2-222-1-1-1-111-2020-1-1-1-1110000000000001100000
χ402222-1222-1-122222-1-2-12-111-12-1-1-1-122-1-2-2-2-200-1-2-211-2-211-1-1-1111122011-2-2-1-11100-2-200-1-122-2-21111112020-1-111-1-1000000000000-1-100000
χ4122-2-22222-2-22-2-2-2-22022200-222-22-2-2-2-200002i−2i2000000002-2-20000000000000002i−2i002i−2i00002-222-2-20000000000002i−2i0000000000002i−2i000
χ4222-2-22222-2-22-2-2-2-22022200-222-22-2-2-2-200002i−2i2000000002-2-20000000000000002i−2i002i−2i0000-22-2-2220000000000002i−2i000000000000−2i2i000
χ4322-2-22222-2-22-2-2-2-22022200-222-22-2-2-2-20000−2i2i2000000002-2-2000000000000000−2i2i00−2i2i00002-222-2-2000000000000−2i2i000000000000−2i2i000
χ4422-2-22222-2-22-2-2-2-22022200-222-22-2-2-2-20000−2i2i2000000002-2-2000000000000000−2i2i00−2i2i0000-22-2-222000000000000−2i2i0000000000002i−2i000
χ452-22-2222-22-2-222-2-2-20222002-2-2-2-2-22-222-22i−2i00200000000-22-200000002-22-2002i−2i002i−2i00002i−2i0000002-20000002i−2i000000000000002i−2i00000
χ462-22-2222-22-2-222-2-2-20222002-2-2-2-2-22-222-2−2i2i00200000000-22-200000002-22-200−2i2i00−2i2i0000−2i2i0000002-2000000−2i2i00000000000000−2i2i00000
χ472-22-2222-22-2-222-2-2-20222002-2-2-2-2-22-22-222i−2i00200000000-22-20000000-22-22002i−2i002i−2i0000−2i2i000000-220000002i−2i00000000000000−2i2i00000
χ482-22-2222-22-2-222-2-2-20222002-2-2-2-2-22-22-22−2i2i00200000000-22-20000000-22-2200−2i2i00−2i2i00002i−2i000000-22000000−2i2i000000000000002i−2i00000
χ492-22-2-122-2-11-222-2-210-12-1−i3i3-1-211112-2-12-22i−2i00-100−i3i300−i3i31-11−i3−i3i3i3000-112-2−i3i3−ii002i−2i003−32i−2i003−33−3-110000−i3i3−ii3−3000000000000−ii00000
χ502-22-2-122-2-11-222-2-210-12-1−i3i3-1-211112-2-12-2−2i2i00-100−i3i300−i3i31-11−i3−i3i3i3000-112-2−i3i3i−i00−2i2i00−33−2i2i00−33−33-110000−i3i3i−i−33000000000000i−i00000
χ512-22-2-122-2-11-222-2-210-12-1−i3i3-1-211112-2-1-222i−2i00-100−i3i300−i3i31-11−i3−i3i3i30001-1-22i3−i3−ii002i−2i003−3−2i2i00−33−331-10000i3−i3−ii3−3000000000000i−i00000
χ522-22-2-122-2-11-222-2-210-12-1−i3i3-1-211112-2-1-22−2i2i00-100−i3i300−i3i31-11−i3−i3i3i30001-1-22i3−i3i−i00−2i2i00−332i−2i003−33−31-10000i3−i3i−i−33000000000000−ii00000
χ532-22-2-122-2-11-222-2-210-12-1i3−i3-1-211112-2-12-22i−2i00-100i3−i300i3−i31-11i3i3−i3−i3000-112-2i3−i3−ii002i−2i00−332i−2i00−33−33-110000i3−i3−ii−33000000000000−ii00000
χ542-22-2-122-2-11-222-2-210-12-1i3−i3-1-211112-2-12-2−2i2i00-100i3−i300i3−i31-11i3i3−i3−i3000-112-2i3−i3i−i00−2i2i003−3−2i2i003−33−3-110000i3−i3i−i3−3000000000000i−i00000
χ552-22-2-122-2-11-222-2-210-12-1i3−i3-1-211112-2-1-222i−2i00-100i3−i300i3−i31-11i3i3−i3−i30001-1-22−i3i3−ii002i−2i00−33−2i2i003−33−31-10000−i3i3−ii−33000000000000i−i00000
χ562-22-2-122-2-11-222-2-210-12-1i3−i3-1-211112-2-1-22−2i2i00-100i3−i300i3−i31-11i3i3−i3−i30001-1-22−i3i3i−i00−2i2i003−32i−2i00−33−331-10000−i3i3i−i3−3000000000000−ii00000
χ5744444-2-2-244-2-2-2-2-244-21-244-21-2-2-2-211-20000441-2-2-2-211-2-2111111100400000000-2-200-2-20000000000000-20-20000001111000000000000000
χ5844444-2-2-244-2-2-2-2-244-21-244-21-2-2-2-211-20000-4-41-2-2-2-211-2-2111111100-4000000002200220000000000000202000000-1-1-1-1000000000000000
χ5944444-2-2-244-2-2-2-2-24-4-21-2-4-4-21-2-2-2-211-200004412222-1-122111-1-1-1-100-400000000-2-200-2-2000000000000020200000011-1-1000000000000000
χ6044444-2-2-244-2-2-2-2-24-4-21-2-4-4-21-2-2-2-211-20000-4-412222-1-122111-1-1-1-1004000000002200220000000000000-20-2000000-1-111000000000000000
χ614444-24-2-2-2-244-2-24-24-2-21-2-2-2-211-2-2-2-2144000014-2-2-2-2-2111111111040-2-2-2-2-2-20000000000000000001100-201100000000000000000000000
χ624444-24-2-2-2-244-2-24-24-2-21-2-2-2-211-2-2-2-21-4-4000014-2-2-2-2-21111111110-40222222000000000000000000-1-10020-1-100000000000000000000000
χ634444-24-2-2-2-244-2-24-2-4-2-2122-2-211-2-2-2-214400001-422222-1-1111-1-1-1-10-40-2-2-2-222000000000000000000110020-1-100000000000000000000000
χ644444-24-2-2-2-244-2-24-2-4-2-2122-2-211-2-2-2-21-4-400001-422222-1-1111-1-1-1-10402222-2-2000000000000000000-1-100-201100000000000000000000000
χ654444-2-244-2-2-2-244-2-241-2-2-2-21-2-2-211-2-2-20044001-2411-2-2-2-21111111400000000-2-200-2-200-2-20000000000-20000011110000000000000000000
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χ674444-2-244-2-2-2-244-2-2-41-2-2221-2-2-211-2-2-200440012-4-1-12222111-1-1-1-1-400000000-2-200-2-20022000000000020000011-1-10000000000000000000
χ684444-2-244-2-2-2-244-2-2-41-2-2221-2-2-211-2-2-200-4-40012-4-1-12222111-1-1-1-140000000022002200-2-20000000000-200000-1-1110000000000000000000
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χ7344-4-44-2-2-2-4-4-2222240-21-20021-22-22-1-1200004i−4i100003-3001-1-13-33-300000000000−2i2i00−2i2i0000000000000000000000i−i3i−3i000000000000000
χ7444-4-44-2-2-2-4-4-2222240-21-20021-22-22-1-1200004i−4i10000-33001-1-1-33-3300000000000−2i2i00−2i2i0000000000000000000000i−i−3i3i000000000000000
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χ7744-4-4-2444224-4-4-4-4-20-24-20024-22-22-4-42000000-200000000-22200000000000000000000000004-4-2-2220000000000000000000000000000000
χ7844-4-4-2444224-4-4-4-4-20-24-20024-22-22-4-42000000-200000000-2220000000000000000000000000-4422-2-20000000000000000000000000000000
χ794-44-444-224-4-44-22-4-404-2-2004222-4-4-22-24-40000-2000000002-2200000004-4-2200000000000000000000-2200000000000000000000000000000
χ804-44-444-224-4-44-22-4-404-2-2004222-4-4-22-2-440000-2000000002-220000000-442-2000000000000000000002-200000000000000000000000000000
χ814-44-44-24-44-42-24-42-40-2-2400-22-4-422-224004i−4i00-2000000002-2200000000000004i−4i00−2i2i00000000000000000000−2i2i000000000000000000000
χ824-44-44-24-44-42-24-42-40-2-2400-22-4-422-22400−4i4i00-2000000002-220000000000000−4i4i002i−2i000000000000000000002i−2i000000000000000000000
χ834-44-4-24-22-22-44-22-420-2-21−2i32i3-22-1-122-2214-40000100−2i32i300i3−i3-11-1i3i3−i3−i3000-22-22−2i32i30000000000000000001-10000i3−i300000000000000000000000
χ844-44-4-24-22-22-44-22-420-2-21−2i32i3-22-1-122-221-440000100−2i32i300i3−i3-11-1i3i3−i3−i30002-22-22i3−2i3000000000000000000-110000−i3i300000000000000000000000
χ854-44-4-24-22-22-44-22-420-2-212i3−2i3-22-1-122-2214-400001002i3−2i300−i3i3-11-1−i3−i3i3i3000-22-222i3−2i30000000000000000001-10000−i3i300000000000000000000000
χ864-44-4-24-22-22-44-22-420-2-212i3−2i3-22-1-122-221-4400001002i3−2i300−i3i3-11-1−i3−i3i3i30002-22-2−2i32i3000000000000000000-110000i3−i300000000000000000000000
χ874-44-4-2-24-4-222-24-42201-2-2−2i32i31222-1-1-22-2004i−4i00100i3−i300−2i32i3-11-1i3i3−i3−i3000000000−2i2i00−2i2i0023−230000000000000000i−i−330000000000000000000
χ884-44-4-2-24-4-222-24-42201-2-2−2i32i31222-1-1-22-200−4i4i00100i3−i300−2i32i3-11-1i3i3−i3−i30000000002i−2i002i−2i00−23230000000000000000−ii3−30000000000000000000
χ894-44-4-2-24-4-222-24-42201-2-22i3−2i31222-1-1-22-2004i−4i00100−i3i3002i3−2i3-11-1−i3−i3i3i3000000000−2i2i00−2i2i00−23230000000000000000i−i3−30000000000000000000
χ904-44-4-2-24-4-222-24-42201-2-22i3−2i31222-1-1-22-200−4i4i00100−i3i3002i3−2i3-11-1−i3−i3i3i30000000002i−2i002i−2i0023−230000000000000000−ii−330000000000000000000
χ914-4-44444-4-44-4-4-444-4044400-4-4-44-44-44-4000000400000000-4-4400000000000000000000000000000000000000000000000000000000000000
χ924-4-4444-22-44-4-42-24-404-2-200-422-2-442-22000000-20000000022-200000000000000000000000000000000000000000000000000000−2i32i30000000
χ934-4-4444-22-44-4-42-24-404-2-200-422-2-442-22000000-20000000022-2000000000000000000000000000000000000000000000000000002i3−2i30000000
χ944-4-444-24-4-4422-44-2-40-2-240022-442-22-2-4000000-20000000022-2000000000000000000000000000000000000000000000000000−2i32i3000000000
χ954-4-444-24-4-4422-44-2-40-2-240022-442-22-2-4000000-20000000022-20000000000000000000000000000000000000000000000000002i3−2i3000000000
χ964-4-44-244-42-2-4-4-44420-24-2002-42-22-2-442000000-20000000022-200000000000000000000000000023−23−23230000000000000000000000000000000
χ974-4-44-244-42-2-4-4-44420-24-2002-42-22-2-442000000-20000000022-2000000000000000000000000000−232323−230000000000000000000000000000000
χ988888-4-4-4-4-4-4-4-4-4-4-4-48222-4-4222222222000000-1-4-4222222-1-1-1-1-1-1-10000000000000000000000000000000000000000000000000000000000
χ998888-4-4-4-4-4-4-4-4-4-4-4-4-822244222222222000000-144-2-2-2-2-2-2-1-1-111110000000000000000000000000000000000000000000000000000000000
χ10088-8-8-48-4-4448-844-8-40-4-42004-42-2-4444-20000002000000002-2-200000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-48844-44-8-84-402-4-400-2-4-442-24440000002000000002-2-200000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-4-444-44444-4022200-222-22-2-2-2-2000000-100006-600-111-33-330000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-4-444-44444-4022200-222-22-2-2-2-2000000-10000-6600-1113-33-30000000000000000000000000000000000000000000000000000000000
χ1048-88-88-4-448-84-4-444-80-42-400-4-244442-2-4000000200000000-22-200000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-44-444-4-44440222−4i34i32-2-2-2-2-22-22000000-1002i3−2i3002i3−2i31-11−i3−i3i3i30000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-44-444-4-444402224i3−4i32-2-2-2-2-22-22000000-100−2i32i300−2i32i31-11i3i3−i3−i30000000000000000000000000000000000000000000000000000000000
χ1078-8-888-4-44-88444-4-4-80-42-4004-24-44-4-224000000200000000-2-2200000000000000000000000000000000000000000000000000000000000000
χ1088-8-88-48-444-4-8-84-4840-4-420044-224-44-4-2000000200000000-2-2200000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-4-48-84-444-88-4402-4-400-244-4-224-44000000200000000-2-2200000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-444-4444-4-44022200-2-2-22-22-22-2000000-10000000011-1−3i33i33i3−3i30000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-444-4444-4-44022200-2-2-22-22-22-2000000-10000000011-13i3−3i3−3i33i30000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).